Enhanced volume phase grating with high dispersion, high diffraction efficiency and low polarization sensitivity

ABSTRACT

An enhanced volume phase diffraction grating provides high dispersion, uniformly high diffraction efficiency and equal diffraction efficiencies for all polarizations across a wide range of wavelengths. In preferred embodiments, the thickness of the volume phase material and the modulation of its refractive index are jointly established to provide equalization of diffraction efficiencies for all polarizations over a wide range of wavelengths. The equalization occurs where the S and P diffraction efficiencies are both at a maximum.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application is a continuation of pending U.S. applicationSer. No. 09/682,007, filed on Jul. 9, 2001.

BACKGROUND OF THE INVENTION

[0002] The telecommunications industry is growing at an explosive paceas a result of the expanding need for the transmitting and receiving ofgreater amounts of information. The industry, in order to meet the needsof the market, has developed a number of technologies that make use ofthe inherent broadband capabilities of fiber optics. One of thesetechnologies is Wavelength Division Multiplexing, or WDM.

[0003] WDM allows many signals to be transmitted simultaneously along asingle optical fiber by sending each signal on a different carrier. Eachcarrier is a light beam of a slightly different wavelength than that ofall of the other carriers. In order to combine these individual carrierbeams into a single beam at the input of the fiber, an opticalmultiplexer (MUX) must be employed. To separate the carriers at thereceiving end of the fiber, an optical de-multiplexer (DEMUX) must beemployed. To be effective and economically practical, a MUX or a DEMUXmust be capable of separating a multi-wavelength light beam into itsindividual wavelength components with a minimum amount of insertion lossand a minimum amount of Polarization Dependent Loss (PDL) and berelatively inexpensive and relatively compact.

[0004] The primary function of a DEMUX is to separate the carrier beamsby wavelength. There are four basic means of providing this function:(1) thin film filters, (2) arrayed waveguides, (3) fiber Bragg gratings,(4) diffraction gratings. Thin film filters use multiple filters, eachtuned to a different wavelength. Separation occurs at each filter alongthe light propagation path. This method is effective for systems with asmall number of channels (one channel corresponds to one carrierwavelength). For systems with large numbers of channels (100 or more)thin film filters are not suitable because the insertion loss isexcessive and the overall system becomes too complex.

[0005] Arrayed waveguides use an array of different length waveguides. Alight beam consisting of multiple carriers, each at a differentwavelength, exiting an input fiber is spread out so that it enters allof the waveguides in the array. The wavelength of each carrier in eachwaveguide, and the length of that waveguide, will determine its phaserelative to the light of the same wavelength exiting all of the otherwaveguides. This phase relationship, in turn, will establish the overallphase distribution of the exiting wavefront for that particularwavelength. That phase distribution will then determine the output portto which this carrier wave will be directed.

[0006] Arrayed waveguides are very complex so that large arrays aredifficult to make and some means of temperature control is generallyrequired. This complexity places a practical upper limit on the numberof channels that can be delivered with arrayed waveguides.

[0007] Fiber Bragg gratings are similar to thin film filters except thatthe filtering is done by a grating created within the fiber. Thewavelength selection is done at each grating within the fiber. FiberBragg gratings have the same insertion loss problem as thin filmfilters—the insertion loss becomes excessive for large numbers ofchannels and, as with thin film filters, the overall system becomesunacceptably complex for a large number of channels.

[0008] All three of the above technologies have a relatively high costper channel.

[0009] The fourth technology, diffraction gratings, has the potentialfor both high performance (large number of channels and low insertionloss) and relatively low cost. A diffraction grating provides separationof a large number of discrete wavelengths by the process of dispersion.An incident beam consisting of multiple carriers of differentwavelengths is dispersed by diffraction as the beam is either reflectedfrom the grating or transmitted through the grating. Each wavelength ofthe exiting beam is reflected or transmitted at a different angle ofdiffraction so that each carrier can enter a different port. This wouldbe the case for a DEMUX. For a MUX, the separate carriers would becombined into a single beam in a process that is essentially the reverseof that described above for a DEMUX.

[0010] The obvious advantage of diffraction gratings over the threeother technologies is that a single, relatively simple device providesthe complete wavelength separation function. Therefore, the cost,complexity and size of the MUX or DEMUX will all be less, yet the numberof channels will be greater.

[0011] There are four types of diffraction gratings but only three aresuitable for WDM applications reflective and transmissive surface reliefgratings and transmissive volume phase gratings. Surface relief gratingscan have relatively high diffraction efficiencies, but generally onlyfor one polarization. This creates a problem in WDM that is known asPolarization Dependent Loss, or PDL. While PDL cannot be eliminated in asurface relief grating, it can be minimized, but only at relatively lowgrating frequencies (roughly 600 lines per mm or less). This low gratingfrequency reduces the dispersion of the grating, making it moredifficult to insert more channels and get good channel separation.

[0012] Transmissive volume phase gratings can also have high diffractionefficiencies but, as in the case of surface relief gratings, this highdiffraction efficiency generally occurs only for one polarization.Therefore, a conventional volume phase grating (VPG) will also exhibithigh PDL. While PDL can be minimized in a conventional VPG, either theoverall diffraction efficiency will be low or the dispersion will below, resulting in either unacceptably high insertion loss or relativelyfewer channels.

[0013] It is obvious that none of the aforementioned technologiesprovides what is desirable in a WDM device—large number of channels, lowinsertion loss and low PDL across the full bandwidth of one of thetelecommunications bands.

SUMMARY OF INVENTION

[0014] Preferred embodiments of the present invention provide a meansfor overcoming the shortcomings of the prior art in WDM devices bycreating an Enhanced Volume Phase Grating (E-VPG) that has highdispersion and uniformly high diffraction efficiency across a broadwavelength range for all polarizations. In the E-VPG, the thickness ofthe volume phase grating material, its bulk index, its index modulationand the angles of incidence and diffraction are all established so thatthe diffraction efficiency for both S-polarization and P-polarizationare simultaneously maximized at the nominal wavelength. The volume phasegrating material is created, coated, exposed and processed so that thedesired values of these four major parameters are obtained.

[0015] A set of equations is developed that will determine these desiredparameters for a number of different possible grating designs. Gratingsin air or gratings attached to one or two prisms (a design oftenreferred to as a Carpenter's prism or grism) can be created using thesedesign equations. Some of the designs will have higher dispersion thanothers but all will have high dispersion and high diffraction efficiencyacross a relatively wide bandwidth for all polarizations.

[0016] By employing a reflective element in the path of the diffractedbeam, the E-VPG can be used in a reflective, double pass mode so thatthe overall dispersion is increased over that of a single E-VPG, whilestill maintaining high overall diffraction efficiency and low PDL.

[0017] An advantage of preferred embodiments of the present inventionover the prior art is that they can provide the advantages ofdiffraction gratings over the three competitive technologies—thin filmfilters, arrayed waveguides, fiber Bragg gratings—without thedisadvantages generally associated with conventional volume phasegratings or surface relief gratings—high PDL and/or low dispersionand/or high insertion loss.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 shows the Wavelength Division Multiplexing portion of atelecommunications system.

[0019]FIG. 2 is a cross-sectional view of an embodiment of the EnhancedVolume Phase Grating of the present invention.

[0020]FIG. 3 is a typical plot of the S and P diffraction efficienciesof a Volume Phase Grating as functions of the index modulation, Δn, fora given effective medium thickness, T, and a given pair of angles ofincidence and diffraction, Θ_(i), and Θ_(d).

[0021]FIG. 4 is a plot of the S and P diffraction efficiencies of aVolume Phase Grating as functions of the index modulation, Δn, for agiven effective medium thickness, T, and a given pair of angles ofincidence and diffraction, Θ_(i), and Θ_(d), where these angles aregreater than those in FIG. 3.

[0022]FIG. 5 is a plot of the S and P diffraction efficiencies of aVolume Phase Grating as functions of the index modulation, Δn, for agiven effective medium thickness, T, and a given pair of angles ofincidence and diffraction, Θ_(i), and Θ_(d), where these angles are lessthan those in FIG. 3.

[0023]FIG. 6 is a plot of the S and P diffraction efficiencies of aVolume Phase Grating as functions of the index modulation, Δn, for aVolume Phase Grating in which the angles of incidence and diffraction,Θ_(i), and Θ_(d), are selected so that the second peak of the Sdiffraction efficiency curve coincides with the first peak of the Pdiffraction efficiency curve.

[0024]FIG. 7 is a plot of the S and P diffraction efficiencies of aVolume Phase Grating as functions of the index modulation, Δn, for aVolume Phase Grating in which the angles of incidence and diffraction,Θ_(i), and Θ_(d), are selected so that the third peak of the Sdiffraction efficiency curve coincides with the second peak of the Pdiffraction efficiency curve.

[0025]FIG. 8 is a plot of the S and P diffraction efficiencies asfunctions of wavelength for the Volume Phase Grating of FIG. 6.

[0026]FIG. 9 is a plot of the S and P diffraction efficiencies asfunctions of the index modulation, Δn, for an Enhanced Volume PhaseGrating of the present invention.

[0027]FIG. 10 is a plot of the S and P diffraction efficiencies asfunctions of wavelength for the Enhanced Volume Phase Grating of thepresent invention.

[0028]FIG. 11 is an embodiment of the present invention in which a prismis used at the entrance and/or exit surface of the grating.

[0029]FIG. 12 is an embodiment of the present invention in which areflective means is provided at the final surface of the exit prism.

[0030]FIG. 13 is an embodiment of the present invention in which areflective means is provided at the exit surface of the grating.

[0031]FIG. 14 is a plot of the S and P diffraction efficiencies asfunctions of wavelength for an embodiment of the present invention inwhich the worst case PDL is reduced.

[0032]FIG. 15 is a plot of the S and P diffraction efficiencies asfunctions of the angle of incidence for an embodiment of the presentinvention in which the Bragg sensitivity is reduced for a double-passdesign.

DETAILED DESCRIPTION

[0033]FIG. 1 shows the Wavelength Division Multiplexing portion of atelecommunications system. The incoming beams from multiple sources(Tx₁, Tx₂, Tx₃, Tx_(n)) with corresponding multiple carrier wavelengths(λ₁, λ₂, λ₃, λ_(n)) are combined into a single beam in a multiplexer(MUX) and transmitted along a single optical fiber 10. At the receivingend of the fiber the de-multiplexer (DEMUX) breaks the single beam upinto many beams, each of a different wavelength (λ₁, λ₂, λ₃, λ_(n)),corresponding to the wavelength of each of the carrier beams at theinput to the MUX. These beams are then directed to the correspondingreceptor elements (Rx₁, Rx₂, Rx₃, Rx_(n)). A first Enhanced Volume PhaseGrating (E-VPG) of the present invention performs the wavelengthcombining function of the MUX. A second E-VPG of the present inventionperforms the wavelength separation function of the DEMUX.

[0034]FIG. 20 shows a cross-sectional view of an E-VPG transmissivediffraction grating, with a general reference number 20. An incidentbeam 22, with a free space wavelength λ is incident on the first surface24 of the cover glass 26 at an angle of incidence (relative to thenormal to the surface 24) of θ_(i) degrees. Upon entering the coverglass, the beam is refracted in accordance with the well known Snell'slaw of refraction. The refracted beam 28 is transmitted to the interfacesurface 30 between the cover glass 26 and the volume phase medium 32,where it is again refracted in accordance with Snell's law. Therefracted beam 34 is propagated into the volume phase medium 32 at anangle of refraction a relative to the normal to the interface surface30.

[0035] Within the volume phase medium 32 there will be a periodicmodulation of refractive index Δn. The surfaces of maximum refractiveindex are called the Bragg surfaces 46. The period of this modulation,measured along the interface surface 30, is designated as d. Theincident beam 34 will be diffracted within the phase medium inaccordance with the grating equation:

λ/nd=sin α+sin β

[0036] where λ is the free space wavelength of the incident beam, d isthe grating spacing measured along the interface surface 30, n is theaverage bulk refractive index of the volume phase medium 32, a is theangle of the incident beam 34 within the volume phase medium 32 relativeto the normal to the interface surface 30 and β is the angle of thediffracted beam 36 within the volume phase medium 32 relative to thenormal to the second interface surface 40. The effective thickness ofthe volume phase medium 32 is T.

[0037] The diffracted beam 36 will be refracted at the interface surface40 between the volume phase medium 32 and the substrate medium 42 inaccordance with Snell's law and transmitted to the exit surface 44 ofthe substrate 42, where it will be once again refracted in accordancewith Snell's law and will exit the substrate 42 at an angle θ_(d)relative to the normal to the exit surface 44.

[0038] In the special, but most common, case where the four surfaces 24,30, 40 and 44 are plane surfaces parallel to each other and therefractive indexes of the external entrance medium and the external exitmedium are the same, then the grating equation can be written as:

λ/n ₀ d=sin θ_(i)+sin θ_(d)

[0039] where n₀ is the refractive index of the entrance/exit medium.

[0040] The angle between the internal incident beam 34 and the Braggsurfaces 46 within the volume phase medium 32 is designated as θ. Whenthe angle between the internal diffracted beam 36 and the Bragg surfaces46 within the volume phase medium 32 is also θ, then the Bragg conditionis said to be satisfied. In the example shown in FIG. 2, the internalangle of diffraction, α, is not equal to the internal angle ofincidence, β. Therefore the Bragg surfaces will be tilted (not normal tosurfaces 30 and 40) as indicated in FIG. 2.

[0041] In a WDM embodiment of the present invention, the wavelength, λ,of the incident beam is the nominal, or center, wavelength of one of thetelecommunications bands. One such communication band is the C band,whose center wavelength is approximately 1546 nm and whose bandwidth isapproximately 37 nm. The external angle of diffraction for the centerwavelength is θ_(d). The angle of diffraction for other wavelengths ofthe particular telecommunications band will be greater than or less thanθ_(d), in accordance with the grating equation.

[0042] In a preferred embodiment of the present invention, the E-VPGgrating 20 is a holographic grating created with a VPG material, such asdichromated gelatin (DCG). Any of several volume phase materials can beused but DCG is well suited for the construction of an E-VPG because itis capable, when properly exposed and processed, of providing very highmodulation of the index of refraction, a key requirement for a goodE-VPG.

[0043] The substrate material 42 on which the volume phase medium 32 iscoated is glass or fused silica, or one of any number of other wellknown transparent materials. The choice of the substrate material willgenerally be determined by the thermal expansion requirements. Thevolume phase medium will generally be sandwiched between two pieces ofthe transparent material—the substrate 42 and a cover, or capping,medium 26 and secured with a transparent optical adhesive, which alsoacts as a sealant to protect the DCG from the environment. The covermedium 26 is glass or fused silica, or one of any number of other wellknown transparent materials.

[0044] The theory of volume phase gratings is well known. Severaltheories exist but the one most applicable for thick gratings withmoderate index modulation and relatively large angles of incidence anddiffraction is the Kogelnik Coupled Wave Theory. While moresophisticated and precise theories exist, they are more complex and addlittle of significant value to the results obtained from the Kogelniktheory when the conditions are such that only the first order diffractedbeam exists and the thickness of the medium is relatively large. Theseare the conditions that pertain to the E-VPG.

[0045] The major VPG parameters in the Kogelnik theory are the averagebulk refractive index, n, of the medium, the effective thickness, T, ofthe medium and the index modulation, Δn of the medium. The entering andexiting beam parameters of interest are the angle of incidence, θ_(i),the angle of diffraction, θ_(d), and the polarization of the incomingbeam. By convention, the polarization direction is defined as thedirection of the electric field in the beam.

[0046] The polarization direction of an optical beam incident on anoptical surface is generally defined relative to the plane of incidence,which is defined as the plane containing the chief ray of the incidentbeam and the normal to the surface at the point of incidence. If thepolarization direction is perpendicular to the plane of incidence, thebeam is said to be S-polarized, from the German word forperpendicular—Senkrecht. If the polarization direction lies in the planeof incidence, the beam is said to be P-polarized (P=parallel). If thebeam is polarized in any other direction, its polarization can always beresolved into components in these two orthogonal directions. Therefore,knowing the effects on the beam of the VPG for both the S-polarizationdirection and the P-polarization direction will be sufficient to providethe effects for any random polarization direction.

[0047] The major parameters of interest in the Kogelnik theory are the Sand P diffraction efficiencies, Es and Ep, where diffraction efficiencyis defined as the ratio of the energy, or power, in the diffracted beam48 to that in the incident beam 22, ignoring the Fresnel reflectionlosses.

[0048] The Kogelnik theory provides the S and P diffraction efficienciesof a VPG as functions of the product of the index modulation, Δn, andthe effective thickness, T, of the medium. Generally, either effectivethickness is assumed to be constant and Δn is varied or Δn is assumed tobe constant and effective thickness is varied. In practice, the firstapproach is the most common—the effective thickness is assumed to beconstant.

[0049] The effective thickness, T, is used instead of the physicalthickness, Tp, because the index modulation, in general, is not constantthroughout the depth of the medium. The exposing and chemical processingof many VPG materials, such as DCG, results in a decrease of Δn withdepth in the medium. It is well known in the art that this variation canbe taken into account by using an effective thickness that is less thanthe physical thickness and then using the assumption that the Δn isconstant over this reduced effective thickness.

[0050]FIG. 3 shows a typical plot of the S and P diffractionefficiencies of a VPG as functions of the index modulation, Δn, for agiven effective thickness, T, and a given pair of angles of incidenceand diffraction. Note that the P efficiency lags the S efficiency as afunction of the index modulation. This is a result of the cosine factorthat exists for the P polarized diffraction efficiency in the Kogelniktheory as shown in the following discussion.

[0051] In the Kogelnik theory, a parameter υ is introduced, where υ isdefined by the following equation:

υ=πΔnT/[λ{square root}(C _(R) C _(S))]  (1)

[0052] where:

[0053] λ is the nominal wavelength of the incident light beam in air

[0054] T is the effective thickness of the VPG medium

[0055] Δn is the peak modulation of the VPG medium

[0056] C_(R) is the incident beam obliquity factor (from the Kogelniktheory)

[0057] C_(S) is the diffracted beam obliquity factor (from the Kogelniktheory)

[0058] C_(R) and C_(S) are both functions of the average bulk refractiveindex, n, of the VPG medium

[0059] The S-polarization diffraction efficiency is then given by thefollowing equation:

E _(S)=sin² υ  (2)

[0060] and the P-polarization diffraction efficiency is given by thefollowing equation:

E _(p)=sin²(υ cos 2θ)  (3)

[0061] So the S-polarization diffraction efficiency is a function onlyof υ, whereas the P-polarization diffraction efficiency is a function ofboth υ and 20, which is the angle between the incident beam 34 and thediffracted beam 36 within the volume phase medium 32. The dependence onυ of the P-polarization diffraction efficiency produces the lag of E_(p)relative to E_(s) in the graph of diffraction efficiencies versus indexmodulation. The angle θ is determined by the angle of incidence, θ_(i),and the angle of diffraction, θ_(d). As these angles increase, the lagwill increase. FIG. 4 shows the S and P diffraction efficiency curvesfor angles of incidence and diffraction that are larger than those inthe example of FIG. 3. Eventually, when the angle of incidence, θ_(i),and the angle of diffraction, θ_(d), are such that the angle between thetwo beams inside the medium, 2θ, is 90 degrees, the amount of lag willbe infinite and the P diffraction efficiency will never rise above zero,no matter how large the value of Δn. In that case, the diffracted beamwill be completely S-polarized.

[0062] Since the P efficiency lags the S efficiency, the two diffractionefficiencies are not, in general, maximum at the same value of Δn. In aVPG that is intended for use in a WDM application, this will result inthree possible scenarios, none of which are desirable.

[0063] First, one could reduce the P-S lag by using relatively smallangles of incidence and diffraction as is done in the prior art (U.S.patent application Ser. No. 09/193,289). The S and P diffractionefficiency curves for this case are shown in FIG. 5. Note that the S andP diffraction efficiency curves intersect at a relatively high value ofdiffraction efficiency. Therefore, the S and P diffraction efficiencieswill be equal and both diffraction efficiencies will be relatively high.The result will be reasonably low insertion loss and relatively low PDLacross a fairly broad wavelength range. (Insertion loss is inverselyrelated to the diffraction efficiency. PDL is directly related to thedifference between the S and P diffraction efficiencies). Thedisadvantage of this approach is that the dispersion will be relativelylow because the angles are relatively small. (The dispersion of adiffraction grating is directly related to the angle between theincident and diffracted beams.)

[0064] In a second case, the angles are increased in order to get moredispersion. Then we have the S and P diffraction efficiency curvessimilar to those shown in FIG. 3. One can then choose to operate at thepeak of the S diffraction efficiency curve so that the insertion lossfor S-polarization will be low. However, since the P diffractionefficiency is low at this value of Δn, the PDL will be very high.

[0065] In a third case, the angles are increased to provide very highdispersion so that we have the situation shown in FIG. 4. However, inthis case, the choice is made to operate at the crossover point of thetwo curves in order to minimize the PDL. But both the S and Pdiffraction efficiencies will be low at this value of Δn. The net resultis that this approach will provide very high dispersion and low PDL butvery high insertion loss.

[0066] So the three cases just described will provide (1) low insertionloss and low PDL but low dispersion; (2) low insertion loss and highdispersion but large PDL; (3) high dispersion and low PDL but very highinsertion loss. None of these three situations is optimum for WDMapplications. What is desired is (a) high dispersion and (b) lowinsertion loss and (c) low PDL.

[0067] One can achieve this desired combination if the angles ofincidence and diffraction are selected so that the P diffractionefficiency curve reaches its first maximum when the S diffractionefficiency curve reaches its second maximum. This situation is shown inFIG. 6. In this case, the S and P diffraction efficiencies are bothequal and both maximum so that the PDL is minimized. In addition, theangles at which this equalization occurs are relatively large so thatthe dispersion is also large. The net result is that the insertion lossis low, the PDL is low and the dispersion is high. That is, we have thedesired combination of all three major grating parameters.

[0068] One can increase the dispersion even further by increasing theangles of incidence and diffraction until S and P maxima farther outalong the An axis coincide. For example, one can select angles ofincidence and diffraction so that the third peak of the S diffractionefficiency curve coincides with the first or second peak of the Pdiffraction efficiency curve, as shown in FIG. 7. This will providegreater dispersion and it will also allow the effective thickness, T, tobe reduced (for a given index modulation, Δn). Higher order combinationsare also possible but these combinations may be more difficult tofabricate.

[0069] In order for the S and P maxima to coincide, the values of Es andEp from equations (2) and (3) must be simultaneously equal to 1. Es willbe equal to 1 when $\upsilon = {\frac{{2s} - 1}{2}\pi}$

[0070] and Ep will be equal to 1 when${{\upsilon \quad {\cos \left( {2\quad \theta} \right)}} = {\frac{{2p} - 1}{2}\pi}},$

[0071] where s and p are integers, 1, 2, 3, . . . The value of cos(2θ)at which the Es and Ep maxima coincide can be found by simply solvingthe above two equations for cos(2θ). The result is equation (4) below:

cos(2θ)=(2p−1)/(2s−1)  (4)

[0072] (Since the cosine of an angle cannot be greater than 1 for anyreal angle, the integer, p, must always be less than the integer, s, inequation (4).)

[0073] where:

[0074] s is the order of the S diffraction efficiency peak (1, 2, 3, . .. ) and p is the order of the P diffraction efficiency peak (1, 2, 3, .. . ),

[0075] θ is the angle between the incident beam and the Bragg planesinside the medium (A Bragg plane is a plane of maximum refractive indexin the medium), and

[0076] 2θ is the angle between the incident beam and the diffracted beaminside the medium.

[0077] Equation (1) can be re-arranged to provide an equation for theindex modulation:${\Delta \quad n} = {\frac{\upsilon \quad \lambda}{\pi \quad T}{\sqrt{C_{R}C_{S}}.}}$

[0078] But from the derivation of Equation (4) above we know that$\upsilon = {\frac{{2s} - 1}{2}\pi}$

[0079] when Es is maximum. Therefore, when Es is maximum,${\Delta \quad n} = {\frac{\lambda}{T}\left( \frac{{2s} - 1}{2} \right)\sqrt{C_{R}C_{S}}}$

[0080] where

[0081] C_(R)=cos α$C_{S} = {{\cos \quad \alpha} - {\frac{\lambda}{n\quad d}{\tan \left( \frac{\beta - \alpha}{2} \right)}}}$

[0082] (See Kogelnik, H. “Coupled Wave Theory for Thick HologramGratings,” Bell System Technical Journal, Vol. 48, No. 9, 1969, Equation23)

[0083] The final result is: $\begin{matrix}\begin{matrix}{{\Delta \quad n} = {\frac{\lambda}{T}\frac{{2s} - 1}{2}\sqrt{C_{R}C_{S}}}} \\{= {\frac{\lambda}{T}\left( \frac{{2s} - 1}{2} \right)\sqrt{\left( {\cos \quad \alpha} \right)\left( {{\cos \quad \alpha} - {\frac{\lambda}{nd}{\tan \left( \frac{\beta - \alpha}{2} \right)}}} \right)}}}\end{matrix} & (5)\end{matrix}$

[0084] where all terms have been previously defined.

[0085] So the value of the index modulation, Δn, at which theS-polarization diffraction efficiency is maximum, for a givenwavelength, index of refraction of the medium and effective thickness ofthe medium, is given by equation (5). Therefore, when equations (4) and(5) are satisfied simultaneously, the S and P diffraction efficiencieswill be maximized simultaneously.

[0086] From FIG. 2 it can be seen that a α+β=2θ, so that Equation (4)can be solved for β, the internal angle of diffraction, to yield:$\begin{matrix}{\beta = {{a\quad {\cos \left( \frac{{2p} - 1}{{2s} - 1} \right)}} - \alpha}} & (6)\end{matrix}$

[0087] Therefore, for given values of the bulk refractive index, n,effective thickness, T and wavelength, λ, and arbitrarily selectedvalues of the integers s and p and the internal angle of incidence, α,the value of the internal angle of diffraction, β, established by Eq.(6) and the value of the index modulation, Δn, established by Eq. 5 willresult in simultaneously maximizing the S-polarization diffractionefficiency, Es, and the P-polarization diffraction efficiency, Ep, at acommon value of the index modulation, Δn.

[0088] This coincidence of the sth peak of the S-polarizationdiffraction efficiency curve and the pth peak of the P-polarizationdiffraction efficiency curve at a common value of the index modulation,Δn, is the major novel property of the Enhanced Volume Phase Grating.FIG. 7 is an example of an Enhanced Volume Phase Grating where the thirdpeak of the S-polarization diffraction efficiency curve coincides withthe second peak of the P-polarization diffraction efficiency curve at anindex modulation value of 0.21.

[0089] Note that coincidence of the sth peak of the S diffractionefficiency curve and the pth peak of the P diffraction efficiency curvewill also occur when the following equation for β is satisfied:$\begin{matrix}{\beta = {180 - {a\quad {\cos \left( \frac{{2p} - 1}{{2s} - 1} \right)}} - \alpha}} & (7)\end{matrix}$

[0090] That is, the S and P diffraction efficiency peaks will coincidewhen the angle between the incident beam and the Bragg planes inside themedium is either θ or 90-θ. In other words, the two angles will lieequally to either side of the zero-P-efficiency angle of 45 degrees.

[0091] The second angle will generally exceed the internal angle oftotal internal reflection (TIR) if the substrate is parallel to the VPGmedium and the external medium is air. This problem can be overcome byusing a dual-prism grism design such as that shown in FIG. 11. This typeof design allows the angles of incidence and diffraction inside themedium to exceed the normal TIR angle.

[0092] The required value of the index modulation, Δn, will be dependenton the effective thickness, T, the wavelength, λ, and the two obliquityfactors, C_(R) and C_(S). The values of the obliquity factors will bedependent on the bulk index of the medium and the external angles ofincidence and diffraction, as established by the Kogelnik theory.

[0093] Designing an Enhanced Volume Phase Grating in Accordance with thePresent Invention

[0094] As an example of the design process for an Enhanced Volume PhaseGrating, consider the simplest case, where s=2 and p=1. Not only is thisthe simplest E-VPG design, it is also the easiest E-VPG to fabricate andis, therefore, the most likely E-VPG to be used in practice.

[0095] Note that the selection of the integer values of s and p iscompletely arbitrary, so long as s>p. The design process would beidentical for any combination of s and p integers. E-VPGs resulting froma selection of larger values of s and p would have greater dispersionbut would be more difficult to fabricate and would require the use ofexternal prisms.

[0096] Once s and p are selected (2 and 1 in this example), the angle ofincidence, θ_(i), must be selected. The angle of incidence, θ_(i), canbe selected to provide a symmetric grating design, where the angle ofdiffraction, θ_(d), is equal to the angle of incidence, θ_(i), or anon-symmetric grating design, where the angle of diffraction, θ_(d), isnot equal to the angle of incidence, θ_(i). The choice is generallygoverned by other factors in the overall system design.

[0097] Once θ_(i) is established, the internal angle of incidence, α,can be determined using the well known Snell's Law and the known bulkrefractive index, n, of the volume phase medium. Then, once thisinternal angle of incidence, α, is determined, equation (6) can be usedto establish the internal angle of diffraction, β. Then Snell's Law canbe used to determine the external angle of diffraction, θ_(d).

[0098] Knowing the internal angle of incidence, α, the internal angle ofdiffraction, β, the bulk refractive index, n, of the volume phase mediumand the free space wavelength, λ, of the incident beam, one can use thefollowing equation, which is a transposition of the grating equationnoted earlier, to determine the grating period, d: $\begin{matrix}{d = {\frac{\lambda}{n\left( {{\sin \quad \alpha} + {\sin \quad \beta}} \right)}.}} & (8)\end{matrix}$

[0099] Furthermore, knowing the external angle of incidence, θ_(i), andthe external angle of diffraction, θ_(d), the construction illuminationgeometry of the E-VPG can be established. In fact, if the applicationwavelength and the construction wavelength for the E-VPG are the same,then θ_(i) and 180+θ_(d) will be the construction angles for the laserbeams used in constructing the E-VPG. If the construction wavelength isnot the same as the application wavelength, as is often the case, thenthe construction angles must be modified in accordance with proceduresthat are well known in the art of fabrication of volume phase gratings(See, for example, the following US patents: U.S. Pat. No. 6,085,980 andU.S. Pat. No. 6,112,990).

[0100] The final step in the fabrication process of the E-VPG is toexpose and process the E-VPG so that the peak index modulation, Δn, isequal to the value calculated in equation (5). Exposure and processingmethods to accomplish this are well known in the art (See, for example,Chang, M. “Dichromated Gelatin of Improved Quality”, Applied Optics,Vol. 10, p. 2250, 1971 and Meyerhofer, D. “Phase Holograms inDichromated Gelatin,” RCA Review, Vol. 35, p. 110, 1972.)

[0101] Note: In an alternative design process, one can select a valuefor the external angle of diffraction, θ_(d), and use Snell's Law todetermine the internal angle of diffraction, β, equation (6) todetermine the internal angle of incidence angle, α and Snell's Law todetermine the external angle of incidence, θ_(i). The constructionprocess and the procedure to establish the peak index modulation, Δn,would be the same as for the case where the angle of incidence, θ_(i),was selected at the outset.

[0102] Satisfying equations (5) and (6) is sufficient to obtain highdiffraction efficiency for both polarizations simultaneously. And theangles needed to satisfy the second of these two equations will resultin high dispersion. However, there is a fourth requirement for a WDMgrating that has made the accomplishment of the present inventionheretofore impossible. The WDM application requires low insertion lossand low PDL across the full width of one of the telecommunicationspassbands. That is, for the C band, the insertion loss and the PDL mustbe acceptably low over the full wavelength range from 1528 nm to 1565nm. That is impossible to achieve In a conventional VPG because of thehigh Bragg angle sensitivity that would result when the necessaryequations are satisfied. Bragg angle sensitivity is the variation ofdiffraction efficiency as a function of either the wavelength or theangle of incidence of the incident beam.

[0103] In a conventional VPG, Δn is typically in the range of 0.05 to0.08. In order to satisfy equation (2) an effective thickness on theorder of 25 to 35 microns would be required. It is well known that Braggangle sensitivity is a strong function of the effective thickness of themedium. FIG. 8 shows the variation of S and P diffraction efficienciesfor an effective medium thickness of 35 microns. The Bragg anglesensitivity is quite large and the resulting PDL at the ends of thepassbands is totally unacceptable for WDM applications.

[0104] The present invention solves this final problem by exposing andprocessing the medium (DCG, in this case) to get a Δn on the order of0.2 or greater. Processing procedures for DCG are well known in the artand processing for high Δn, while difficult, is an extension of knownDCG processing methods.

[0105] In a typical embodiment of the present invention, the medium(DCG) is spin coated on a glass or fused silica substrate to a physicalthickness that is on the order of 15 microns. It is exposed in aconventional dual-beam holographic grating fabrication process using alaser with a wavelength to which the DCG is responsive. It is thenprocessed in a sequence of alcohol water baths using well-known DCGprocessing procedures. After drying and edge stripping to provide anadhesive o-ring seal when capped, the actual gratings are then dicedfrom the larger grating, and then sealed (capped) with a cover glass.

[0106] In this particular embodiment of the present invention, theexposure and processing of the grating will yield a final effectivethickness of approximately 9 to 10 microns.

[0107]FIG. 9 shows the S and P diffraction efficiency curves for oneexample of an Enhanced Volume Phase Grating of the present inventionwith an effective thickness of 9 microns and with the angles ofincidence and diffraction selected to satisfy equation (4). Thepost-processing bulk refractive index of the medium is approximately1.27, but may vary from 1.2 or less to 1.4 or greater.

[0108]FIG. 10 shows the variation of the S and P diffractionefficiencies as functions of wavelength for this particular E-VPG. Notethat both efficiencies fall off only slightly to either side of thenominal wavelength and the difference in falloff of the twopolarizations is very small so that PDL will be low across the fullbandwidth.

[0109] This design now satisfies all of the major requirements for aneffective diffraction grating for WDM applications—high dispersion, lowinsertion loss, low PDL—all across the full passband.

[0110] An extension of this invention uses higher numbers for p and s inEquations 4 and 5. This will result in gratings that have higherdispersion than the grating described above. In general, higher p and snumbers will require the use of a grism design.

[0111] A further extension of this invention is shown in FIG. 11. Afirst prism 50 is used at the entrance surface 64 of the grating 52 anda second prism 54 is used at the exit surface 68 of the grating 52. Theincident beam 56 may be normal to the entrance surface 58 of the prism50 or it may be at some non-normal angle, depending on the designrequirements of the grating and the system in which it is to be used.Similarly, the exit beam 62 may be normal to the exit surface 60 of thesecond prism or it may be at some non-normal angle, depending on thedesign requirements of the grating and the system in which it is to beused. The two prisms are not necessarily equal in geometric shape orrefractive index. In the extreme, the refractive index of one of theprisms could be 1, so that the two-prism embodiment becomes asingle-prism embodiment.

[0112] A prism is required for higher order grating designs (largervalues of s and p) but it may also be advantageous in the primary orderdesign for packaging reasons or mechanical stability.

[0113] A further extension of this invention is shown in FIG. 12. Thisextension of the present invention is similar to that shown in FIG. 11but with the addition of a mirror 84 attached to the final surface 80 ofthe exit prism 74. The mirror 84 reflects the diffracted beam 89 backinto the grating 72 for a second pass 90, thereby increasing the overalldispersion. The double-pass design concept for conventional(non-enhanced) volume phase gratings has been described in the prior art(U.S. patent application Ser. No. 09/193,289).

[0114] A further extension of this invention is shown in FIG. 13. Thisextension of the present invention uses a mirror 98 attached to, orlocated in the vicinity of, the final surface 102 of the grating 92. Themirror 98 reflects the diffracted beam 91, back into the grating at, ornear, normal incidence for a second pass 94, through the grating 92thereby doubling the dispersion. Such a design functions like a Littrowgrating, but with higher dispersion for a given grating spatialfrequency.

[0115] In a further extension of this invention, the substrate 42 andthe cover glass 26 are both coated with an anti-reflection (AR) coatingso that at the nominal wavelength, λ, the overall loss forS-polarization is slightly greater than the overall loss forP-polarization. The resultant S and P wavelength Bragg sensitivitycurves are shown in FIG. 14. Note that the PDL is now non-zero at thenominal wavelength but it is also less at the wavelengths correspondingto the ends of the passband. That is, the worst-case PDL has beenreduced.

[0116] In yet another extension of this invention, the substrate 42 andthe cover glass 26 are both coated with an AR coating so that at thenominal wavelength, λ, the overall loss for S-polarization is greaterthan the overall loss for P-polarization by an amount that is greaterthan that of the prior extension discussed above. This additional lossimproves the performance of the E-VPG grating in a two-pass design. Thiscan be seen in FIG. 15. This graph shows the variation in the S and Pdiffraction efficiencies as a function of the angle of incidence of thebeam. In a two-pass design, the angle of incidence at the second passthrough the grating varies as a function of the wavelength due to thedispersion resulting from the first pass through the grating. At theextremes of the passband, the angle of incidence will be such as tolower the S and P diffraction efficiencies. Increasing the nominal lossfor the S beam, as shown, will reduce the worst case PDL.

[0117] In a preferred embodiment of this invention, the angle ofincidence, a, in the volume phase medium 32 will equal the angle ofdiffraction, β, in the volume phase medium 32 at the nominal wavelength,λ. While other embodiments that can satisfy equations (4) and (5) (or(5) and (6)) will be obvious to one skilled in the art, this particularembodiment has two significant advantages: (a) the dispersion will bemaximized compared to other combinations of angles that satisfyequations (4) and (5); (b) the Bragg surfaces 46 will be normal to thesurface 40 of the substrate 42, which simplifies the fabricationprocess. However, embodiments in which the angles α and β are not equalmay have geometric or other advantages and are therefore included asextensions of the art exemplified in the preferred embodiment.

[0118] While there have been described what are considered to bepreferred embodiments of the present invention, variations andmodifications will occur to those skilled in the arts once they becomeacquainted with the basic concepts of the invention. Therefore, it isintended that the appended claims shall be construed to include both thepreferred embodiments and all such variations and modifications as fallwithin the true spirit and scope of the invention.

What is claimed is:
 1. An enhanced volume phase grating, comprising: asubstrate; a transparent cover; and a volume phase medium between thesubstrate and the transparent cover, wherein the volume phase medium hasa thickness, T, a surface, and a bulk refractive index, the bulkrefractive index is periodically modulated in a direction parallel tothe surface of the volume phase medium, with a peak value of refractiveindex equal to n+Δn, where Δn is the peak modulation of said bulkrefractive index and n is a refractive index, the periodic sequence ofpeak values of said bulk refractive index throughout the thickness ofthe volume phase medium provides a periodic structure of Bragg surfaceswithin said volume phase medium with a period, d, where the period, d,satisfies${d = \frac{\lambda}{n\left( {{\sin \quad \alpha} + {\sin \quad \beta}} \right)}},$

where λ is the nominal free-space wavelength for which said enhancedvolume phase grating is designed,${{\Delta \quad n} = {\frac{\lambda}{T}\left( \frac{{2s} - 1}{2} \right)\sqrt{\left( {\cos \quad \alpha} \right)\left( {{\cos \quad \alpha} - {\frac{\lambda}{n\quad d}\quad {\tan \left( \frac{\beta - \alpha}{2} \right)}}} \right)}}},$

s is a positive integer satisfying s>p, where p is another positiveinteger, θ_(i) is an arbitrary external angle of incidence, and β is aninternal angle of diffraction that satisfies $\begin{matrix}{\beta = {{{either}\quad a\quad {\cos \left( \frac{{2p} - 1}{{2s} - 1} \right)}} - \alpha}} & {or} & {{180 - {a\quad {\cos \left( \frac{{2p} - 1}{{2s} - 1} \right)}} - \alpha},}\end{matrix}$ where${\alpha = {a\quad {\sin \left( \frac{\sin \quad \theta_{i}}{n} \right)}}},$

whereby the S-polarization diffraction efficiency and the P-polarizationdiffraction efficiency of said enhanced volume phase grating, whenilluminated by an incident beam of said nominal free-space wavelength,λ, at said external angle of incidence, θ_(i), are simultaneouslymaximized at a common value of the product ΔnT, simultaneouslyminimizing insertion loss and PDL.
 2. The enhanced volume phase gratingof claim 1, wherein said volume phase medium is dichromated gelatin.